Design a method that can compute the following partial sum accurately for very large N, S_(N) = \ sum_(n = 1)^N ((-1)^(n-1))/(n). From Calculus, we know that \lim_(N-> \infty )S_(N) is a finite number. Since successive terms in the sum have opposite signs and become increasingly close together as n grows, there may be a danger of increasing error through cancellation. How can you evaluate the sum in a way that avoids this danger? (Hint. Use additions only.)
Design a method that can compute the following partial sum accurately for very large N, S_(N) = \ sum_(n = 1)^N ((-1)^(n-1))/(n). From Calculus, we know that \lim_(N-> \infty )S_(N) is a finite number. Since successive terms in the sum have opposite signs and become increasingly close together as n grows, there may be a danger of increasing error through cancellation. How can you evaluate the sum in a way that avoids this danger? (Hint. Use additions only.)
Chapter9: Sequences, Probability And Counting Theory
Section9.4: Series And Their Notations
Problem 1SE: What is an nth partial sum?
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Transcribed Image Text:Design a method that can compute the following partial sum accurately for very large N, S_(N) = \
sum_(n = 1)^N ((-1) ^ (n-1))/(n). From Calculus, we know that \lim_(N-> \infty )S_(N) is a finite
number. Since successive terms in the sum have opposite signs and become increasingly close
together as n grows, there may be a danger of increasing error through cancellation. How can you
evaluate the sum in a way that avoids this danger? (Hint. Use additions only.)
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